This has already been requested a few years ago and I suggest you Follow the original item for the jQuery widget which is where the feature must be implemented first before it can make it into the ASP.NET Core wrappers: https://feedback.telerik.com/kendo-jquery-ui/1360229-listbox-with-crud. I've already added your vote for it.

To be candid, the low popularity it has (4 requests for 2+ years) makes it unlikely to become a built-in feature soon. At the moment, you can perform the CRUD operations manually by calling your own endpoints in a fashion similar to this demo: https://demos.telerik.com/aspnet-core/listbox/drag-and-drop or this one for the plain jQuery widgets: https://demos.telerik.com/kendo-ui/listbox/drag-and-drop.